costFunctionReg.m

function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

    hx = sigmoid(X*theta);
    reg_theta = theta; 
    reg_theta(1) = 0;
    J = (-1/m)*(y'*log(hx) + (1-y)'*log(1-hx)) + (lambda/(2*m))*(reg_theta'*reg_theta);

    grad = (1/m)*(X'*(hx-y)) + (lambda/m)*reg_theta;


% =============================================================

end